THIBON , Jean-Yves

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The Hopf algebra of word-quasi-symmetric functions ($\WQSym$), a noncommutative generalization of the Hopf algebra of quasi-symmetric functions, can be endowed with an internal product that has several compatibility properties with the other operations on $\WQSym$. This extends constructions familiar and central in the theory of free Lie...

We obtain a complete and minimal set of 170 generators for the algebra of SL(2, C )×4- covariants of a binary quadrilinear form. Interpreted in terms of a four qubit system, this describes in particular the algebraic varieties formed by the orbits of local filtering operations in its projective Hilbert space. Also, this sheds some light on the...

We investigate deformations of the shuffle Hopf algebra structure Sh(A) which can be defined on the tensor algebra over a commutative algebra A. Such deformations, leading for example to the quasi-shuffle algebra QSh(A), can be interpreted as natural transformations of the functor Sh, regarded as a functor from commutative nonunital algebras to...

We investigate deformations of the shuffle Hopf algebra structure Sh(A) which can be defined on the tensor algebra over a commutative algebra A. Such deformations, leading for example to the quasi-shuffle algebra QSh(A), can be interpreted as natural transformations of the functor Sh, regarded as a functor from commutative nonunital algebras to...

We study the invariant theory of trilinear forms over a three-dimensional complex vector space, and apply it to investigate the behavior of pure entangled three-partite qutrit states and their normal forms under local filtering operations (SLOCC). We describe the orbit space of the SLOCC group SLs3,Cd33 both in its affine and projective...